Title: A positive answer on the existence of correlations between positive earthquake magnitude differences

Abstract: The identification of patterns in space, time, and magnitude, which could potentially encode the subsequent earthquake magnitude, represents a significant challenge in earthquake forecasting. A pivotal aspect of this endeavor involves the search for correlations between earthquake magnitudes, a task greatly hindered by the incompleteness of instrumental catalogs. A novel strategy to address this challenge is provided by the groundbreaking observation by Van der Elst (Journal of Geophysical Research: Solid Earth, 2021), that positive magnitude differences, under certain conditions, remain unaffected by incompleteness. In this letter we adopt this strategy which provides a clear and unambiguous proof regarding the existence of correlations between subsequent positive magnitude differences. Our results are consistent with a time-dependent b-value in the Gutenberg-Richter law, significantly enhancing existing models for seismic forecasting.